What if they split S? They avoid your shot and actually gain a little speed. Then what?
He gains kinetic energy (speed) but loses Potential energy (altitude). I personally would loop back up and dive into him aggressively to keep the pressure on and prevent him from regaining that altitude. If he keeps doing split-s's then eventually he'll run out of altitude to convert into speed, and eventually he'll run out of speed if you can keep the pressure on an prevent him from gaining speed back.
I know I have had to use a split-s when being defensive against a BnZ attacker, but I only use it when I have no speed to work with. The Defenders objective when fighting someone with more altitude is to first neutralize that altitude advantage by either slowly working his way up to him or waiting for the attacker to make a mistake. A split-s will get you more speed but will give the attacker an even bigger altitude advantage unless you can regain that altitude (which a good pilot won't let you do). If you can't get to their altitude then the only times you are going to get to go offensive is the very brief moment when he overshoots, and that's not a very large window of opportunity to get a good shot in.
I was just going off the assumption that the defender was at speed in my previous post. In those scenarios their first move will tell you a lot about how skilled of a pilot you are fighting. If I can see they have decent enough speed to maneuver (250mph or more) and their first move is some sort of turn to preserve as much altitude as possible, then I know I'm fighting someone who probably knows what they're doing. If they immediately roll inverted and split-s then it's more often than not he's not quite a skilled pilot yet.